Elasticsearch之中文分词器插件es-ik（博主推荐）
前提
什么是倒排索引？
Elasticsearch之分词器的作用
Elasticsearch之分词器的工作流程
Elasticsearch之停用词
Elasticsearch之中文分词器
Elasticsearch之几个重要的分词器
elasticsearch官方默认的分词插件
1、elasticsearch官方默认的分词插件，对中文分词效果不理想。
比如，我现在，拿个具体实例来展现下，验证为什么，es官网提供的分词插件对中文分词而言，效果差。
[hadoop@HadoopMaster elasticsearch-2.4.3]$ jps
2044 Jps
1979 Elasticsearch
[hadoop@HadoopMaster elasticsearch-2.4.3]$ pwd
/home/hadoop/app/elasticsearch-2.4.3
[hadoop@HadoopMaster elasticsearch-2.4.3]$ curl 'http://192.168.80.10:9200/zhouls/_analyze?pretty=true' -d '{"text":"这里是好记性不如烂笔头感叹号的博客园"}'
{
"tokens" : [ {
"token" : "这",
"start_offset" : 0,
"end_offset" : 1,
"type" : "<IDEOGRAPHIC>",
"position" : 0
}, {
"token" : "里",
"start_offset" : 1,
"end_offset" : 2,
"type" : "<IDEOGRAPHIC>",
"position" : 1
}, {
"token" : "是",
"start_offset" : 2,
"end_offset" : 3,
"type" : "<IDEOGRAPHIC>",
"position" : 2
}, {
"token" : "好",
"start_offset" : 3,
"end_offset" : 4,
"type" : "<IDEOGRAPHIC>",
"position" : 3
}, {
"token" : "记",
"start_offset" : 4,
"end_offset" : 5,
"type" : "<IDEOGRAPHIC>",
"position" : 4
}, {
"token" : "性",
"start_offset" : 5,
"end_offset" : 6,
"type" : "<IDEOGRAPHIC>",
"position" : 5
}, {
"token" : "不",
"start_offset" : 6,
"end_offset" : 7,
"type" : "<IDEOGRAPHIC>",
"position" : 6
}, {
"token" : "如",
"start_offset" : 7,
"end_offset" : 8,
"type" : "<IDEOGRAPHIC>",
"position" : 7
}, {
"token" : "烂",
"start_offset" : 8,
"end_offset" : 9,
"type" : "<IDEOGRAPHIC>",
"position" : 8
}, {
"token" : "笔",
"start_offset" : 9,
"end_offset" : 10,
"type" : "<IDEOGRAPHIC>",
"position" : 9
}, {
"token" : "头",
"start_offset" : 10,
"end_offset" : 11,
"type" : "<IDEOGRAPHIC>",
"position" : 10
}, {
"token" : "感",
"start_offset" : 11,
"end_offset" : 12,
"type" : "<IDEOGRAPHIC>",
"position" : 11
}, {
"token" : "叹",
"start_offset" : 12,
"end_offset" : 13,
"type" : "<IDEOGRAPHIC>",
"position" : 12
}, {
"token" : "号",
"start_offset" : 13,
"end_offset" : 14,
"type" : "<IDEOGRAPHIC>",
"position" : 13
}, {
"token" : "的",
"start_offset" : 14,
"end_offset" : 15,
"type" : "<IDEOGRAPHIC>",
"position" : 14
}, {
"token" : "博",
"start_offset" : 15,
"end_offset" : 16,
"type" : "<IDEOGRAPHIC>",
"position" : 15
}, {
"token" : "客",
"start_offset" : 16,
"end_offset" : 17,
"type" : "<IDEOGRAPHIC>",
"position" : 16
}, {
"token" : "园",
"start_offset" : 17,
"end_offset" : 18,
"type" : "<IDEOGRAPHIC>",
"position" : 17
} ]
}
[hadoop@HadoopMaster elasticsearch-2.4.3]$
总结
如果直接使用Elasticsearch的朋友在处理中文内容的搜索时，肯定会遇到很尴尬的问题——中文词语被分成了一个一个的汉字，当用Kibana作图的时候，按照term来分组，结果一个汉字被分成了一组。
这是因为使用了Elasticsearch中默认的标准分词器，这个分词器在处理中文的时候会把中文单词切分成一个一个的汉字，因此引入es之中文的分词器插件es-ik就能解决这个问题。
如何集成IK分词工具
总的流程如下：
第一步：下载es的IK插件https://github.com/medcl/elasticsearch-analysis-ik/tree/2.x
第二步：使用maven对下载的es-ik源码进行编译(mvn clean package -DskipTests)
第三步：把编译后的target/releases下的elasticsearch-analysis-ik-1.10.3.zip文件拷贝到ES_HOME/plugins/ik目录下面，然后使用unzip命令解压
如果unzip命令不存在，则安装：yum install -y unzip
第四步：重启es服务
第五步：测试分词效果： curl 'http://your ip:9200/zhouls/_analyze?analyzer=ik_max_word&pretty=true' -d '{"text":"这里是好记性不如烂笔头感叹号的博客们"}'
注意：若你是单节点的es集群的话，则只需在一台部署es-ik。若比如像我这里的话，是3台，则需在三台都部署es-ik，且配置要一样。
elasticsearch-analysis-ik-1.10.0.zip 对应于 elasticsearch-2.4.0
elasticsearch-analysis-ik-1.10.3.zip 对应于 elasticsearch-2.4.3
我这里，已经给大家准备好了，以下是我的CSDN账号。下载好了，大家可以去下载。
http://download.csdn.net/detail/u010106732/9890897 http://download.csdn.net/detail/u010106732/9890918
https://github.com/medcl/elasticsearch-analysis-ik/tree/v1.10.0
第一步: 在浏览器里，输入https://github.com/
第二步：https://github.com/search?utf8=%E2%9C%93&q=elasticsearch-ik
第三步：https://github.com/medcl/elasticsearch-analysis-ik ，点击2.x 。当然也有一些人在用2.4.0版本，都适用。若你是使用5.X，则自己对号入座即可，这个很简单。
第四步：https://github.com/medcl/elasticsearch-analysis-ik/tree/2.x 得到
第五步：找到之后，点击，下载，这里选择离线安装。
第六步：将Elasticsearch之中文分词器插件es-ik的压缩包解压下，初步认识下其目录结构，比如我这里放到D盘下来认识下。并为后续的maven编译做基础。
第七步：用本地安装好的maven来编译
Microsoft Windows [版本 6.1.7601]
版权所有 (c) 2009 Microsoft Corporation。保留所有权利。
C:\Users\Administrator>cd D:\elasticsearch-analysis-ik-2.x
C:\Users\Administrator>d:
D:\elasticsearch-analysis-ik-2.x>mvn
得到，
D:\elasticsearch-analysis-ik-2.x>mvn clean package -DskipTests
[INFO] Scanning for projects...
[INFO]
[INFO] ------------------------------------------------------------------------
[INFO] Building elasticsearch-analysis-ik 1.10.4
[INFO] ------------------------------------------------------------------------
Downloading: http://maven.aliyun.com/nexus/content/repositories/central/org/apac
he/maven/plugins/maven-enforcer-plugin/1.0/maven-enforcer-plugin-1.0.pom
Downloaded: http://maven.aliyun.com/nexus/content/repositories/central/org/apach
e/maven/plugins/maven-enforcer-plugin/1.0/maven-enforcer-plugin-1.0.pom (7 KB at
2.5 KB/sec)
Downloading: http://maven.aliyun.com/nexus/content/repositories/central/org/apac
he/maven/enforcer/enforcer/1.0/enforcer-1.0.pom
Downloaded: http://maven.aliyun.com/nexus/content/repositories/central/org/apach
e/maven/enforcer/enforcer/1.0/enforcer-1.0.pom (12 KB at 19.5 KB/sec)
Downloading: http://maven.aliyun.com/nexus/content/repositories/central/org/apac
he/maven/maven-parent/17/maven-parent-17.pom
Downloaded: http://maven.aliyun.com/nexus/content/repositories/central/org/apach
e/maven/maven-parent/17/maven-parent-17.pom (25 KB at 41.9 KB/sec)
Downloading: http://maven.aliyun.com/nexus/content/repositories/central/org/apac
he/maven/plugins/maven-enforcer-plugin/1.0/maven-enforcer-plugin-1.0.jar
Downloaded: http://maven.aliyun.com/nexus/content/repositories/central/org/apach
e/maven/plugins/maven-enforcer-plugin/1.0/maven-enforcer-plugin-1.0.jar (22 KB a
t 44.2 KB/sec)
Downloading: http://maven.aliyun.com/nexus/content/repositories/central/org/apac
he/maven/plugins/maven-compiler-plugin/3.5.1/maven-compiler-plugin-3.5.1.pom
Downloaded: http://maven.aliyun.com/nexus/content/repositories/central/org/apach
e/maven/plugins/maven-compiler-plugin/3.5.1/maven-compiler-plugin-3.5.1.pom (10
KB at 35.3 KB/sec)
Downloading: http://maven.aliyun.com/nexus/content/repositories/central/org/apac
he/maven/plugins/maven-plugins/28/maven-plugins-28.pom
Downloaded: http://maven.aliyun.com/nexus/content/repositories/central/org/apach
e/maven/plugins/maven-plugins/28/maven-plugins-28.pom (12 KB at 42.1 KB/sec)
Downloading: http://maven.aliyun.com/nexus/content/repositories/central/org/apac
he/maven/maven-parent/27/maven-parent-27.pom
Downloaded: http://maven.aliyun.com/nexus/content/repositories/central/org/apach
e/maven/maven-parent/27/maven-parent-27.pom (40 KB at 94.0 KB/sec)
Downloading: http://maven.aliyun.com/nexus/content/repositories/central/org/apac
he/apache/17/apache-17.pom
Downloaded: http://maven.aliyun.com/nexus/content/repositories/central/org/apach
需要等待一会儿，这个根据自己的网速快慢。
Downloaded: http://maven.aliyun.com/nexus/content/repositories/central/org/apach
e/maven/maven-archiver/2.4/maven-archiver-2.4.jar (20 KB at 19.8 KB/sec)
Downloading: http://maven.aliyun.com/nexus/content/repositories/central/org/apac
he/maven/shared/maven-repository-builder/1.0-alpha-2/maven-repository-builder-1.
0-alpha-2.jar
Downloaded: http://maven.aliyun.com/nexus/content/repositories/central/org/apach
e/maven/maven-project/2.0.4/maven-project-2.0.4.jar (107 KB at 84.7 KB/sec)
Downloaded: http://maven.aliyun.com/nexus/content/repositories/central/org/codeh
aus/plexus/plexus-utils/2.0.1/plexus-utils-2.0.1.jar (217 KB at 158.7 KB/sec)
Downloaded: http://maven.aliyun.com/nexus/content/repositories/central/org/apach
e/maven/shared/maven-repository-builder/1.0-alpha-2/maven-repository-builder-1.0
-alpha-2.jar (23 KB at 16.4 KB/sec)
Downloaded: http://maven.aliyun.com/nexus/content/repositories/central/org/apach
e/maven/maven-model/2.0.4/maven-model-2.0.4.jar (79 KB at 54.3 KB/sec)
Downloaded: http://maven.aliyun.com/nexus/content/repositories/central/org/apach
e/maven/maven-artifact/2.0.4/maven-artifact-2.0.4.jar (79 KB at 52.9 KB/sec)
[INFO] Reading assembly descriptor: D:\elasticsearch-analysis-ik-2.x/src/main/as
semblies/plugin.xml
[INFO] Building zip: D:\elasticsearch-analysis-ik-2.x\target\releases\elasticsea
rch-analysis-ik-1.10.4.zip
[INFO] ------------------------------------------------------------------------
[INFO] BUILD SUCCESS
[INFO] ------------------------------------------------------------------------
[INFO] Total time: 01:22 min
[INFO] Finished at: 2017-02-25T14:48:40+08:00
[INFO] Final Memory: 35M/609M
[INFO] ------------------------------------------------------------------------
D:\elasticsearch-analysis-ik-2.x>
成功，得到。
这里，需要本地（即windows系统）里，提前安装好maven，需要来编译。若没安装的博友，请移步，见
Eclipse下Maven新建项目、自动打依赖jar包（包含普通项目和Web项目）
最后得到是，
第八步：将最后编译好的，分别上传到3台机器里。$ES_HOME/plugins/ik 目录下,注意需要新建ik目录。
[hadoop@HadoopSlave1 elasticsearch-2.4.3]$ pwd
/home/hadoop/app/elasticsearch-2.4.3
[hadoop@HadoopSlave1 elasticsearch-2.4.3]$ ll
total 56
drwxrwxr-x. 2 hadoop hadoop 4096 Feb 22 01:37 bin
drwxrwxr-x. 3 hadoop hadoop 4096 Feb 22 22:43 config
drwxrwxr-x. 3 hadoop hadoop 4096 Feb 22 07:07 data
drwxrwxr-x. 2 hadoop hadoop 4096 Feb 22 01:37 lib
-rw-rw-r--. 1 hadoop hadoop 11358 Aug 24 2016 LICENSE.txt
drwxrwxr-x. 2 hadoop hadoop 4096 Feb 25 05:15 logs
drwxrwxr-x. 5 hadoop hadoop 4096 Dec 8 00:41 modules
-rw-rw-r--. 1 hadoop hadoop 150 Aug 24 2016 NOTICE.txt
drwxrwxr-x. 4 hadoop hadoop 4096 Feb 22 06:02 plugins
-rw-rw-r--. 1 hadoop hadoop 8700 Aug 24 2016 README.textile
[hadoop@HadoopSlave1 elasticsearch-2.4.3]$ cd plugins/
[hadoop@HadoopSlave1 plugins]$ ll
total 8
drwxrwxr-x. 5 hadoop hadoop 4096 Feb 22 06:02 head
drwxrwxr-x. 8 hadoop hadoop 4096 Feb 22 06:02 kopf
[hadoop@HadoopSlave1 plugins]$ mkdir ik
[hadoop@HadoopSlave1 plugins]$ pwd
/home/hadoop/app/elasticsearch-2.4.3/plugins
[hadoop@HadoopSlave1 plugins]$ ll
total 12
drwxrwxr-x. 5 hadoop hadoop 4096 Feb 22 06:02 head
drwxrwxr-x. 2 hadoop hadoop 4096 Feb 25 06:18 ik
drwxrwxr-x. 8 hadoop hadoop 4096 Feb 22 06:02 kopf
[hadoop@HadoopSlave1 plugins]$ cd ik/
[hadoop@HadoopSlave1 ik]$ pwd
/home/hadoop/app/elasticsearch-2.4.3/plugins/ik
[hadoop@HadoopSlave1 ik]$ rz
[hadoop@HadoopSlave1 ik]$ ll
total 4400
-rw-r--r--. 1 hadoop hadoop 4505518 Jan 15 08:59 elasticsearch-analysis-ik-1.10.3.zip
[hadoop@HadoopSlave1 ik]$
第九步：关闭es服务进程
[hadoop@HadoopSlave1 ik]$ jps
1874 Elasticsearch
2078 Jps
[hadoop@HadoopSlave1 ik]$ kill -9 1874
[hadoop@HadoopSlave1 ik]$ jps
2089 Jps
[hadoop@HadoopSlave1 ik]$
第十步：使用unzip命令解压，如果unzip命令不存在，则安装：yum install -y unzip。
[hadoop@HadoopSlave1 ik]$ unzip elasticsearch-analysis-ik-1.10.3.zip
Archive: elasticsearch-analysis-ik-1.10.3.zip
inflating: elasticsearch-analysis-ik-1.10.3.jar
inflating: httpclient-4.5.2.jar
inflating: httpcore-4.4.4.jar
inflating: commons-logging-1.2.jar
inflating: commons-codec-1.9.jar
inflating: plugin-descriptor.properties
creating: config/
creating: config/custom/
inflating: config/custom/ext_stopword.dic
inflating: config/custom/mydict.dic
inflating: config/custom/single_word.dic
inflating: config/custom/single_word_full.dic
inflating: config/custom/single_word_low_freq.dic
inflating: config/custom/sougou.dic
inflating: config/IKAnalyzer.cfg.xml
inflating: config/main.dic
inflating: config/preposition.dic
inflating: config/quantifier.dic
inflating: config/stopword.dic
inflating: config/suffix.dic
inflating: config/surname.dic
[hadoop@HadoopSlave1 ik]$ ll
total 5828
-rw-r--r--. 1 hadoop hadoop 263965 Dec 1 2015 commons-codec-1.9.jar
-rw-r--r--. 1 hadoop hadoop 61829 Dec 1 2015 commons-logging-1.2.jar
drwxr-xr-x. 3 hadoop hadoop 4096 Jan 1 12:46 config
-rw-r--r--. 1 hadoop hadoop 55998 Jan 1 13:27 elasticsearch-analysis-ik-1.10.3.jar
-rw-r--r--. 1 hadoop hadoop 4505518 Jan 15 08:59 elasticsearch-analysis-ik-1.10.3.zip
-rw-r--r--. 1 hadoop hadoop 736658 Jan 1 13:26 httpclient-4.5.2.jar
-rw-r--r--. 1 hadoop hadoop 326724 Jan 1 13:07 httpcore-4.4.4.jar
-rw-r--r--. 1 hadoop hadoop 2667 Jan 1 13:27 plugin-descriptor.properties
[hadoop@HadoopSlave1 ik]$
同理，其他两台也是。
第十一步：重启三台机器的es服务进程
其实，若想更具体地，看得，es安装中文分词器es-ik之后，的变化情况，直接，在$ES_HOME下，执行bin/elasticsearch。当然，我这里只是给你展示下而已，还是用bin/elasticsearch -d在后台启动吧！
第十二步：测试，安装了es中文分词插件es-ik之后的对中文分词效果
ik_max_word方式来分词测试
[hadoop@HadoopMaster elasticsearch-2.4.3]$ pwd
/home/hadoop/app/elasticsearch-2.4.3
[hadoop@HadoopMaster elasticsearch-2.4.3]$ curl 'http://192.168.80.10:9200/zhouls/_analyze?analyzer=ik_max_word&pretty=true' -d '{"text":"这里是好记性不如烂笔头感叹号的博客园"}'
{
"tokens" : [ {
"token" : "这里是",
"start_offset" : 0,
"end_offset" : 3,
"type" : "CN_WORD",
"position" : 0
}, {
"token" : "这里",
"start_offset" : 0,
"end_offset" : 2,
"type" : "CN_WORD",
"position" : 1
}, {
"token" : "里",
"start_offset" : 1,
"end_offset" : 2,
"type" : "CN_WORD",
"position" : 2
}, {
"token" : "好记",
"start_offset" : 3,
"end_offset" : 5,
"type" : "CN_WORD",
"position" : 3
}, {
"token" : "记性",
"start_offset" : 4,
"end_offset" : 6,
"type" : "CN_WORD",
"position" : 4
}, {
"token" : "不如",
"start_offset" : 6,
"end_offset" : 8,
"type" : "CN_WORD",
"position" : 5
}, {
"token" : "烂",
"start_offset" : 8,
"end_offset" : 9,
"type" : "CN_CHAR",
"position" : 6
}, {
"token" : "笔头",
"start_offset" : 9,
"end_offset" : 11,
"type" : "CN_WORD",
"position" : 7
}, {
"token" : "笔",
"start_offset" : 9,
"end_offset" : 10,
"type" : "CN_WORD",
"position" : 8
}, {
"token" : "头",
"start_offset" : 10,
"end_offset" : 11,
"type" : "CN_CHAR",
"position" : 9
}, {
"token" : "感叹号",
"start_offset" : 11,
"end_offset" : 14,
"type" : "CN_WORD",
"position" : 10
}, {
"token" : "感叹",
"start_offset" : 11,
"end_offset" : 13,
"type" : "CN_WORD",
"position" : 11
}, {
"token" : "叹号",
"start_offset" : 12,
"end_offset" : 14,
"type" : "CN_WORD",
"position" : 12
}, {
"token" : "叹",
"start_offset" : 12,
"end_offset" : 13,
"type" : "CN_WORD",
"position" : 13
}, {
"token" : "号",
"start_offset" : 13,
"end_offset" : 14,
"type" : "CN_CHAR",
"position" : 14
}, {
"token" : "博客园",
"start_offset" : 15,
"end_offset" : 18,
"type" : "CN_WORD",
"position" : 15
}, {
"token" : "博客",
"start_offset" : 15,
"end_offset" : 17,
"type" : "CN_WORD",
"position" : 16
}, {
"token" : "园",
"start_offset" : 17,
"end_offset" : 18,
"type" : "CN_CHAR",
"position" : 17
} ]
}
[hadoop@HadoopMaster elasticsearch-2.4.3]$
[hadoop@HadoopMaster elasticsearch-2.4.3]$ curl 'http://192.168.80.10:9200/zhouls/_analyze?analyzer=ik_max_word&pretty=true' -d '{"text":"我们是大数据开发技术人员"}'
{
"tokens" : [ {
"token" : "我们",
"start_offset" : 0,
"end_offset" : 2,
"type" : "CN_WORD",
"position" : 0
}, {
"token" : "大数",
"start_offset" : 3,
"end_offset" : 5,
"type" : "CN_WORD",
"position" : 1
}, {
"token" : "数据",
"start_offset" : 4,
"end_offset" : 6,
"type" : "CN_WORD",
"position" : 2
}, {
"token" : "开发",
"start_offset" : 6,
"end_offset" : 8,
"type" : "CN_WORD",
"position" : 3
}, {
"token" : "发",
"start_offset" : 7,
"end_offset" : 8,
"type" : "CN_WORD",
"position" : 4
}, {
"token" : "技术人员",
"start_offset" : 8,
"end_offset" : 12,
"type" : "CN_WORD",
"position" : 5
}, {
"token" : "技术",
"start_offset" : 8,
"end_offset" : 10,
"type" : "CN_WORD",
"position" : 6
}, {
"token" : "人员",
"start_offset" : 10,
"end_offset" : 12,
"type" : "CN_WORD",
"position" : 7
} ]
}
[hadoop@HadoopMaster elasticsearch-2.4.3]$
可以看出，成功分词了且效果更好！
其实，啊，为什么“是”没有了呢?是因为es的中文分词器插件es-ik的过滤停止词的贡献！请移步，如下
Elasticsearch之IKAnalyzer的过滤停止词
es官方文档提供的ik_max_word和ik_smart解释
https://github.com/medcl/elasticsearch-analysis-ik/tree/2.x
ik_smart方式来分词测试
[hadoop@HadoopMaster elasticsearch-2.4.3]$ curl 'http://192.168.80.10:9200/zhouls/_analyze?analyzer=ik_smart&pretty=true' -d '{"text":"这里是好记性不如烂笔头感叹号的博客园"}'
{
"tokens" : [ {
"token" : "这里是",
"start_offset" : 0,
"end_offset" : 3,
"type" : "CN_WORD",
"position" : 0
}, {
"token" : "好",
"start_offset" : 3,
"end_offset" : 4,
"type" : "CN_CHAR",
"position" : 1
}, {
"token" : "记性",
"start_offset" : 4,
"end_offset" : 6,
"type" : "CN_WORD",
"position" : 2
}, {
"token" : "不如",
"start_offset" : 6,
"end_offset" : 8,
"type" : "CN_WORD",
"position" : 3
}, {
"token" : "烂",
"start_offset" : 8,
"end_offset" : 9,
"type" : "CN_CHAR",
"position" : 4
}, {
"token" : "笔头",
"start_offset" : 9,
"end_offset" : 11,
"type" : "CN_WORD",
"position" : 5
}, {
"token" : "感叹号",
"start_offset" : 11,
"end_offset" : 14,
"type" : "CN_WORD",
"position" : 6
}, {
"token" : "博客园",
"start_offset" : 15,
"end_offset" : 18,
"type" : "CN_WORD",
"position" : 7
} ]
}
[hadoop@HadoopMaster elasticsearch-2.4.3]$
[hadoop@HadoopMaster elasticsearch-2.4.3]$ curl 'http://192.168.80.10:9200/zhouls/_analyze?analyzer=ik_smart&pretty=true' -d '{"text":"我们是大数据开发技术人员"}'
{
"tokens" : [ {
"token" : "我们",
"start_offset" : 0,
"end_offset" : 2,
"type" : "CN_WORD",
"position" : 0
}, {
"token" : "大",
"start_offset" : 3,
"end_offset" : 4,
"type" : "CN_CHAR",
"position" : 1
}, {
"token" : "数据",
"start_offset" : 4,
"end_offset" : 6,
"type" : "CN_WORD",
"position" : 2
}, {
"token" : "开发",
"start_offset" : 6,
"end_offset" : 8,
"type" : "CN_WORD",
"position" : 3
}, {
"token" : "技术人员",
"start_offset" : 8,
"end_offset" : 12,
"type" : "CN_WORD",
"position" : 4
} ]
}
[hadoop@HadoopMaster elasticsearch-2.4.3]$
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